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arXiv · 1710.00323

Correlation of boundary behavior of conjugate harmonic functions

Vladimir Ryazanov
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Abstract

It is established that if a harmonic function $u$ on the unit disk $\mathbb D$ in $\mathbb C$ has angular limits on a measurable set $E$ of the unit circle $\partial\mathbb D$, then its conjugate harmonic function $v$ in $\mathbb D$ also has angular limits a.e. on $E$ and both boundary functions are finite a.e. and measurable on $E$. The result is extended to arbitrary Jordan domains with rectifiable boundaries in terms of angular limits and of the natural parameter.

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Vladimir Ryazanov. 2017-10-01. Correlation of boundary behavior of conjugate harmonic functions. https://arxiv.org/abs/1710.00323

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